Least Common Multiple (LCM) of 101 and 175
The least common multiple (LCM) of 101 and 175 is 17675.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 101 and 175?
First, calculate the GCD of 101 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 175 = 0 remainder 101 |
| 2 | 175 ÷ 101 = 1 remainder 74 |
| 3 | 101 ÷ 74 = 1 remainder 27 |
| 4 | 74 ÷ 27 = 2 remainder 20 |
| 5 | 27 ÷ 20 = 1 remainder 7 |
| 6 | 20 ÷ 7 = 2 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 85 | 14705 |
| 78 and 113 | 8814 |
| 164 and 39 | 6396 |
| 46 and 88 | 2024 |
| 18 and 135 | 270 |